Liam Fox reiterated at a fringe event that there would be no commitment on the rights of the 2 million EU citizens.
Photograph: Carl Court/Getty Images

The uncertain status of EU nationals living in the UK is “one of our main cards” in the Brexit negotiations with the bloc, Liam Fox has said.

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Speaking at the Conservative party conference in Birmingham, the international trade secretary reiterated that no commitment would be given on the rights of 2 million EU citizens to remain in the UK until reciprocal rights were agreed for British citizens in Europe.

Fox, who was speaking at a fringe event, said the government would “like to be able to give a reassurance to EU nationals in the UK, but that depends on reciprocation by other countries”.

He said any other strategy “would be to hand over one of our main cards in the negotiations and doesn’t necessarily make sense at this point”.

Hinting that a scenario could emerge where EU nationals currently in the UK were not given automatic leave to remain, Fox said: “If we do [negotiations] from the premise that the EU ‘ever closer union’ project is more important than the people, and those who go against it must be punished, we will not get such a good outcome.

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“That’s what the skill of our government will be tested on, if we can get the former, and not lead Europe into the latter.”

The prime minister, Theresa May, has previously said she would expect to guarantee the right to remain for all EU citizens currently living in the UK but stressed that she also wanted to achieve the best deal for Britons living in the EU.

Research from Oxford University’s Migration Observatory in June found three-quarters of EU citizens working in the UK would not meet current visa requirements for non-EU overseas workers.

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Labour MP Chuka Umunna, a supporter of the pro-EU Open Britain campaign, said Fox “needs to understand that he is talking about people not poker chips”.

He added: “These crass remarks would leave even Nigel Farage shamefaced. Instead of gambling with their future, Liam Fox and his government colleagues should do the decent thing and give assurances to all EU nationals living here that they will have the right to stay.”